On the ?-multiple Charlier polynomials - Ozarslan, Mehmet Ali; Baran, Gizem (Springer, 2021)
The main aim of this paper is to define and investigate more general multiple Charlier polynomials on the linear lattice omega N={0,omega,2 omega,...}, omega is an element of R. We call these polynomials omega-multiple Charlier polynomials. Some of their properties, such as the raising operator, the Rodrigues formula, an explicit representation and a generating function are obtained. Also an (r+1)th order difference equation is given. As an example we consider the case omega=3/2 and define 3/2-multiple Charlier polynomials. It is also mentioned that, in the case omega=1, the obtained results coincide with the existing results of multiple Charlier polynomials.
Keywords: Multiple orthogonal polynomials; omega-multiple Charlier polynomials; Appell polynomials; Hypergeometric function; Rodrigues formula; Generating function; Difference equation; 33C45; 33D50; 33E50